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The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
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The correct answer is:
96
In a dictionary, the words at each stage are arranged in aiphabetical order.
In the given problem, we must consider the words beginning with $\mathrm{C}, \mathrm{C}, \mathrm{H}, I, \mathrm{N}, \mathrm{O}$ in order.
So. Number of words starting with $C C=4 !$
Number of words starting with $\mathrm{CH}=4!$
Number of words starting with $\mathrm{Cl}=4!$
Number of words starting with $\mathrm{CN}=4!$
Next word staring with CO ie. COCHIN = 1
$\therefore$ Required number of words $=4 \times 41=96$
In the given problem, we must consider the words beginning with $\mathrm{C}, \mathrm{C}, \mathrm{H}, I, \mathrm{N}, \mathrm{O}$ in order.
So. Number of words starting with $C C=4 !$
Number of words starting with $\mathrm{CH}=4!$
Number of words starting with $\mathrm{Cl}=4!$
Number of words starting with $\mathrm{CN}=4!$
Next word staring with CO ie. COCHIN = 1
$\therefore$ Required number of words $=4 \times 41=96$
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